How to Solve Proportions: Cross Multiply Method + Free Calculator
Proportions show that two ratios are equal — the same idea behind scaling a recipe, reading a map, or solving homework problems like “if 3 costs $12, what do 7 cost?” A free proportion calculator finds the missing number in a/b = c/d so you can skip the algebra when you are in a hurry.
This guide explains cross-multiplication with clear examples, then shows how to use the ToolMars solver for any unknown.
Solve any missing value in a/b = c/d
Free cross-multiply proportion calculator — instant, private, no signup.
What Is a Proportion?
A proportion says two ratios are equivalent:
That means a is to b as c is to d. If three values are known, you can always find the fourth.
How to Cross-Multiply
Cross-multiplication turns a proportion into a simple equation:
Example: Solve x / 4 = 6 / 8.
- Cross-multiply: x × 8 = 4 × 6
- Simplify: 8x = 24
- Divide: x = 3
The same steps work no matter which letter is missing — a, b, c, or d.
Everyday Examples
Where proportions show up
- Recipes: If 2 cups of flour make 12 cookies, how much flour for 30 cookies?
- Maps: 1 inch = 5 miles — how far is a 3.2-inch route?
- Shopping: 3 items for $15 → cost of 7 items at the same rate
- Use the ToolMars proportion calculator to check any of these in seconds.
Ratio vs Proportion (Quick Difference)
A ratio compares two amounts (3:5 or 3/5). A proportion says two ratios are equal (3/5 = 6/10). If you only have one comparison, you have a ratio; if you set two comparisons equal, you have a proportion.
Solve any missing value in a/b = c/d
Free cross-multiply proportion calculator — instant, private, no signup.
Frequently Asked Questions
How do you solve a proportion?
Cross-multiply (a × d = b × c), then isolate the unknown value.
What is the difference between a ratio and a proportion?
A ratio compares two quantities; a proportion states that two ratios are equal.
Can a proportion calculator find any missing value?
Yes — choose which of a, b, c, or d is unknown and enter the other three.
Where are proportions used in real life?
Cooking, maps, unit conversion, shopping unit rates, and geometry scale problems.
What if one of the numbers is zero?
You cannot divide by zero. Recheck inputs if a denominator would be zero.